Question

Find the ratio a : b : c if a + 2b - c = 0 & 2a - b + c = 0 .

Answer 1

Given : a + 2b - c = 0 & 2a - b + c = 0 .

To Find :   Ratio a : b : c

Solution:

a + 2b  - c  =0     Eq1

2a - b + c  = 0     Eq2

Adding eq 1  & eq 2

=> 3a  + b  = 0

=> 3a  =  - b

=> a/b  =  - 1/3

=> a : b  =  - 1 : `3

putting b = - 3a  in Eq1

=> a + 2(-3a)   - c  = 0

=> a - 6a   = c

=>  -5a = c

=> a/c  =  - 1/5

=> a : c  = - 1 : 5

a : b  =  - 1 : 3  

a : c  = - 1 : 5    

a : b :   c  =  -1  : 3  : 5

Lets verify

a = - 1  , b = 3  , c  = 5

a  + 2b - c  =   -1  + 6 + 5 = 0

2a - b + c  = -2  - 3 +  5  = 0

a = 1  , b = -3  , c = -5

a  + 2b - c  =   1  - 6 + 5 =  0

2a - b + c  =   2  + 3 -  5  = 0

a : b :   c  =  -1  : 3  : 5

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Answer 2

a : b : c  =  3 : 1  : 5

Step-by-step explanation:

a  + 2b - c = 0 ----(1)

So c = a + 2b -----(3)

2a - b + c  = 0 ----(2)

Substituting 3 in 2, we get:

2a-b = a + 2b

a = 3b ----(4)

Substituting 4 in 3, we get:

c = 3b + 2b = 5b ----(5)

So writing a, b and c in terms of b, we get:

a : b : c = 3b : b : 5b = 3: 1: 5

Let's check this using equation 1.

a + 2b - c = 3 + 2 - 5 = 0

Hence proved.